Low-Temperature Heat Capacity and Entropy of Diammonium Orthophosphate Basil B. Luff,* Robert B. Reed, and Robert H. Nash Division of Chemical Development, Tennessee Valley Authority, Muscle Shoals, Alabama 35660
The low-temperature heat capacity of diammonium orthophosphate, (NH4)2HP04,was measured over the temperature range 8-316 K by adiabatic calorimetry. The heat capacity, C,; entropy, So;and Planck function, (Go - H o " ) / T ,at 298.15 K were calculated to be 42.82, 42.30, and -19.53 cal mol-' deg-", respectively. The accuracy of the measurements was established by comparing measured values of the heat capacity of pure benzoic acid with those reported by the National Bureau of Standards. In the continuing program of measurement of thermodynamic and thermochemical properties of materials of interest in fertilizer technology, the heat capacity of diammonium orthophosphate, (NH4)2HP04,was measured by adiabatic calorimetry over the temperature range 8-316 K. Related thermodynamic properties were derived. Materials and Apparatus Reagent-grade diammonium phosphate was dissolved in distilled water to make a 71 % solution and the solution was filtered. The stirred filtrate was treated dropwise with methanol (25 parts of methanol per 100 parts of solution) to precipitate diammonium phosphate. The precipitate then was recrystallized by the same procedure to give a material that had the correct composition but contained large voids in the crystals. The purified diammonium phosphate was used to prepare a 21 % solution with distilled water and the pH was adjusted to 8.05 (Z),the ambient temperature was maintained by cooling, methanol was dropped into the solution to the point of cloudiness, and the solution was placed in a refrigerator at about 0 OC for crystallization.The crystals were filtered off and the procedure was repeated with the filtrate to obtain a second crop of crystals. The crystals were washed on the filter with acetone and airdried. The first crop of crystals contained voids, but the second crop was relatively free of voids. Chemical analysis showed the material to contain 21.2% N, 53.8% P205, and 0.05% H20 (stoichiometric: 21.21 ?h N, 53.74% P205). Petrographic examination showed it to be homogeneous as moderately large, well-developed crystals. Inclusions, which appeared to be both air and mother liquor, made up about 0.5 % of the total volume of the material. Preliminary tests showed that the material lost weight slowly over P205 at mmHg; the calorimeter was filled and dried under this pressure for 5 h. The calorimeter charge was 59.9555 g or 0.454 014 mol of (NH4)2HP04;the weight was corrected for bouyancy in air on the basis of a density of 1.61 g ~ r n (-4~) , and the gram formula weight was taken as 132.0565. Its heat capacity ranged from 32% of the total at 10 K to 64% at 300 K. The air in the calorimeter was removed and replaced with the same mass of helium used in measurements on the empty calorimeter; the helium facilitated heat transfer and thermal equilibrium. The adiabatic calorimeter and the method of operation have been described (5). The defined calorie was taken as 4.1840 absolute J and the ice point as 273.15 K. The measured heat capacities were corrected for curvature (3) and for a small dif418
Journal of Chemicaland Engineering Data, Vol. 21, No. 4, 1976
ference in the amount of eutectic solder relative to the empty calorimeter. Because small temperature differences were important, temperatures were measured to four decimal places, but these were rounded to two decimal places in the final tabulation. The heat capacities below 10 K were read from a large scale plot of Cp/ T against that extrapolated smoothly to 0 K. Observed molal heat capacities are shown in Table I. Smoothed heat cap,acity and derived functions at round values of temper-
Table I. Observed Heat Capacity (cal K - l mol-') of Diammonium Orthophosphate CP
8.70 8.73 9.85 10.10 11.25 11.68 12.97 13.66 14.96 15.80 17.10 18.04 19.48 20.63 22.17 24.02 25.06 27.69 28.20 31.25 31.66 35.00 35.35 38.93 39.22 43.17 43.42 47.76 47.98 52.55 52.73 55.78 57.02 59.17 61.59 63.91 66.48 68.94 71.64 74.37 77.32 80.12 80.78 84.34 86.63
0.1479 0.0915 0.1308 0.1352 0.1893 0.2018 0.3038 0.3624 0.4936 0.5828 0.7377 0.8597 1.058 1.227 1.474 1.797 1.970 2.443 2.535 3.122 3.204 3.85 1 3.920 4.640 4.696 5.486 5.538 6.457 6.508 7.511 7.549 8.283 8.570 9.045 9.517 9.985 10.43 10.85 11.30 11.80 12.34 12.87 13.00 13.66 14.08
89.96 92.61 95.76 98.74 101.72 105.01 107.84 111.19 113.90 117.31 119.91 123.39 125.90 129.43 131.86 135.64 137.99 141.84 144.23 148.02 150.58 154.20 156.87 160.38 163.16 166.58 169.45 172.79 175.76 179.02 181.93 185.12 188.13 191.24 194.35 196.06 196.23 197.40 200.86 202.13 206.85 208.24 212.88 214.39 218.96
14.66 15.12 15.65 16.15 16.66 17.21 17.69 18.24 18.69 19.25 19.67 20.23 20.62 21.20 21.60 22.17 22.55 23.17 23.55 24.14 24.49 25.01 25.39 25.9 1 26.30 26.79 27.20 27.67 28.08 28.52 28.91 29.36 29.75 30.16 30.57 30.79 30.81 30.95 31.41 31.57 32.16 32.34 32.91 33.10 33.65
220.58 225.07 226.81 231.23 232.95 237.30 239.12 243.41 245.33 248.34 249.56 251.46 254.43 255.62 257.50 260.44 261.61 263.60 266.50 267.64 269.73 270.54 272.48 273.72 274.42 275.07 275.79 276.25 277.25 279.87 282.23 283.22 285.93 288.26 289.24 292.04 294.33 295.3 1 298.08 299.16 300.83 303.96 306.99 310.09 313.07 316.14
33.85 34.40 34.60 35.15 35.37 35.89 36.12 36.61 36.85 37.20 37.34 37.55 37.90 38.02 38.25 38.58 38.77 38.94 39.29 39.42 39.64 39.76 39.98 40.13 40.16 40.21 40.32 40.37 40.45 40.83 41.07 41.12 41.43 41.74 41.80 42.16 42.40 42.47 42.84 42.90 43.10 43.47 43.76 44.09 44.38 44.68
Table Ill. Heat Capacity of Benzoic Acid
Table II. Molal Thermodynamic Properties of Diammonium Orthophosphate __
C,, cal K-' mol-'
~
T,K 5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 273.15 298.15
c,,
cal K-'
0.0152 0.1308 0.4972 1.128 1.952 2.883 3.848 4.846 5.872 6.950 9.205 11.03 12.85 14.67 16.37 18.04 19.68 2 1.29 22.87 24.41 25.85 27.28 28.66 30.00 31.29 32.56 33.78 35.00 36.22 37.39 38.55 39.68 40.79 41.91 43.02 44.09 40.03 42.82
S, cal K-'
W - H,', cal
-(GOH,")IT, cal K-'
0.0051 0.0420 0.1538 0.3785 0.7158 1.153 1.670 2.248 2.878 3.552 5.021 6.581 8.172 9.792 11.43 13.06 14.71 16.34 17.98 19.61 21.23 22.84 24.44 26.03 27.60 29.16 30.70 32.23 33.74 35.24 36.73 38.21 39.67 41.12 42.56 43.99 38.67 42.30
0.0191 0.3 166 1.756 5.735 13.37 25.43 42.25 63.98 90.76 122.8 203.7 305.1 424.5 562.2 717.4 889.5 1078 1283 1504 1740 1992 2257 2537 2830 3137 3456 3788 4132 4488 4856 5236 5627 6029 6443 6867 7303 5752 6788
0.0013 0.0103 0.0367 0.0918 0.1811 0.3054 0.4626 0.6490 0.8614 1.096 1.626 2.222 2.866 3.545 4.252 4.978 5.720 6.475 7.238 8.009 8.785 9.564 10.35 11.13 11.91 12.70 13.48 14.26 15.04 15.82 16.60 17.37 18.14 18.91 19.67 20.43 17.61 19.53
T K 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 28 0 290 300 310
0
0.06
-
This laboratory
0.4596 2.629 5.239 7.572 9.441 10.97 12.25 13.35 14.37 15.28 16.18 17.09 17.99 18.90 19.81 20.73 21.68 22.63 23.60 24.59 25.60 26.62 27.67 28.73 29.81 30.89 31.98 33.08 34.18 35.29 36.40
0.5110 2.648 5.282 7.593 9.460 10.98 12.24 13.35 14.38 15.29 16.19 17.09 17.99 18.89 19.81 20.74 21.68 22.64 23.60 24.60 25.60 26.62 27.66 28.74 29.81 30.89 31.98 33.06 34.17 35.27 36.39 1
I
1
1
1
005
P
004
8
003
2
002
-V
ature are shown in Table II. The deviations of the observed heat capacity values from the smoothed curve are shown in Figure 1.
,I+ I x
NBS
E
8 5
aoi W O -001
0"
-0.02
-
-004
,
-003
Heat Capacity of a Standard Sample of Benzoic Acid In order to verify the overall accuracy of our technique, measurements were made on the heat capacity of pure benzoic acid made available by the National Bureau of Standards in conjunction with the program of the Calorimetry Conference. A sample of 60.6145 g (in vacuo) of benzoic acid was utilized. The results are compared with the values reported by Ginnings and Furukawa ( 7) in Table Ill. Literature Cited (1) Ginnings, D. G.,Furukawa, G. T., J. Am. Chem. SOC.,75, 522 (1953). (2) Lenfesty. F. A,, Brosheer, J. C.. J. Chem. Eng. Data, 5, 152 (1960). (3) Scott, R. B. Meyers, C. H.,Rands, Jr., R. D., Brickwedde. F. G., Bekkadahl. N., J. Res. Nat. Bur. Stand., 35,39-85 (1945).
8
-005 -0.06
0
50
I 100
1
1
1
1
I50
203
250
300
1
TEMPERATURE, K
Figure 1. Deviations of observed heat capacities from smoothed values for diammonium orthophosphate.
(4) Smith, J. P., Lehr, J. R., Brown, W. E., Acta Crystallogr., 10, 709 (1957). (5) Wakefield, 2. T.. Luff, B. B., Kohler, J. J., J. Chem. fng. Data. 17, 94 (1972). Received for review January 30, 1976. Accepted May 27, 1976.
Journal of Chemicaland Engineering Data, Vol. 21, No. 4, 1976
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